Simplify sixth root of (64a^12)/(729b^6)

$\sqrt[6]{\frac{64 a^{12}}{729 b^{6}}}$

Rewrite $64 a^{12}$ as ${(2 a^{2})}^{6}$ .

$\sqrt[6]{\frac{{(2 a^{2})}^{6}}{729 b^{6}}}$

Rewrite $729 b^{6}$ as ${(3 b)}^{6}$ .

$\sqrt[6]{\frac{{(2 a^{2})}^{6}}{{(3 b)}^{6}}}$

Rewrite $\frac{{(2 a^{2})}^{6}}{{(3 b)}^{6}}$ as ${(\frac{2 a^{2}}{3 b})}^{6}$ .

$\sqrt[6]{{(\frac{2 a^{2}}{3 b})}^{6}}$

Pull terms out from under the radical, assuming positive real numbers.

$\frac{2 a^{2}}{3 b}$